Projection of a model matrix on the orthogonal complement of a trend or curvature.
The columns of a model matrix M is projected on the
orthogonal complement to the matrix (1,t),
resp. (1,t,t^2).
Orthogonality is w.r.t. an inner product defined by the positive
definite matrix matrix diag(weight). Non-diagonal matrices
defining the inner product is not supported.
detrend( M, t, weight = rep(1, nrow(M)) ) decurve( M, t, weight = rep(1, nrow(M)) )
M |
A model matrix. |
t |
The trend defining a subspace. A numerical vector of length
|
weight |
Weights defining the inner product of vectors |
The functions are intended to be used in construction of particular parametrizations of age-period-cohort models.
detrend returns full-rank matrix with columns orthogonal to
(1,t);
decurve returns full-rank matrix with columns orthogonal to
(1,t,t^2).
Bendix Carstensen, Steno Diabetes Center Copenhagen, http://bendixcarstensen.com, with essential help from Peter Dalgaard.
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